 Solution

The bare packed-sphere estimate exceeds $2.1\times 10^5\mathrm{pN}\mathrm{nm}$ by approximately $659$; subtracting the estimated extended-rod self-energy still leaves a factor of about $629$. The dominant missing effect is electrostatic screening: mobile positive counterions accompany the negatively charged DNA, greatly reducing long-range repulsion. Counterion condensation can further reduce its effective electric charge. Treating the genome's bare charge as uncompensated throughout and outside a $20\mathrm{nm}$ sphere therefore grossly overestimates its long-range electrostatic energy.

An optical tweezers measurement integrates an imposed force over a displacement. A reversible extraction or packaging comparison concerns a free energy difference relative to the unconfined DNA and ionic reservoirs. It can include entropy, bending and hydration contributions; dissipative pulling can add further work. Extraction can also be assisted by stored internal free energy, so the sign of externally supplied work requires the experimental convention. Here the supplied positive value is compared as an energy magnitude.